Basic Research Program

Particle-Scale Distribution of Soil Moisture in Porous Media17 April 2008

Dr. Chris Kees and Dr. Matthew FarthingCoastal and Hydraulics Laboratory

Purpose: To provide a multi-scale theoretical

and computational model of variably saturated granular/porous media that will improve our ability to perform engineering-scale analyses.

Product/Results:Theoretical and computational

modeling frameworks for air/water/particle systems.

New constitutive relations for macroscopic models of porous media.

Payoff:Understanding how the microscopic

properties of variably saturated media relate to engineering scale properties will lead to improved ability to detect subsurface features, to build reliable structures, and to predict transport in soils.

Schedule & Cost

Total$738K

MILESTONES Prior FY08 FY09 FY10Years

Army ($K)

Other

Initial Plan/Prep

Particle-Scale Theory

Particle-Scale Simulator

Three-phase Theory

Three-phase Simulator

Multiscale Theory

Multiscale Simulator

Particle-Scale Distribution of Soil Moisture in Porous Materials

Status:Basic6.1

$738KTotal Army

Program

227 261 250

What is the Problem? – We don’t understand the macroscopic structural, hydraulic, thermal, electromagnetic, and chemical properties of variably saturated soils. These properties affect our ability to detect subsurface targets and features, build structures, and predict chemical species transport in soils.

What are the barriers to solving the problem? – Accurately measuring thermodynamic conjugate variables in physical experiments under dynamic conditions, as required for formulation of fundamentally sound constitutive relationships, is not possible. Quantities such as phase pressures, surface tension, fluid phase distribution, fluid phase kinetic and potential energies cannot be independently measured at the pore scale.  

Collaboration across ERDC, commercial firms and/or academia –

Ernest Berney (GSL) - Physics of granular mediaClint Willson (LSU), - Particle scale measurementsTim Kelley (NCSU) - Multilevel solvers and analysisMasa Prodanovic(UT, Austin) - Pore-scale modelingDavid DiCarlo(UT, Austin) - Pore-scale theory/experimentClint Dawson(UT, Austin) - Finite element analysisGraham Carey(UT, Austin) - Finite element analysisCasey Miller(UNC, Chapel Hill) ) - Macroscale modelingHigh Fidelity Vessel Effects Project (CHL) Countermine phenomenology (GSL) Institute for Maneuverability and Terrain Physics (ITL)

What is innovative about this work? The use of particle-scale continuum fluid mechanics simulations that explicitly model the separate phases and the fluid-water and fluid-solid interfaces. The coupling of those models to discrete element models of granular materials to facilitate multi-scale numerical modeling of these systems.

What is your publication plan? FY07 - Mini-symposium on near surface air/water flow at U.S.

National Congress on Computational Mechanics (July). FY08 - Computer Methods in Applied Mechanics and

Engineering (in review). FY09 - Journal of Computational Physics (In preparation),

Multiscale Modeling and Simulation (SIAM).

Particle-Scale Distribution of Soil Moisture in Porous Materials

How will you overcome these barriers? – Apply state-of-the-art computational methods to rigorous continuum thermo-mechanical models of the interaction of air and water phases in granular materials; collaborate with experimentalists and numerical analysis specialists from academia.

What are the results of this research and what is its value? – A multiscale theoretical and computational modeling capability for variably saturated granular materials. The ability to calculate macroscopic properties from particle-scale measurements and/or use simulations to supplement experimental methods in complex three-dimensional settings where direct observation of all physical quantities is not possible; a computational multiscale framework that can be used to carry out fundamentally sound engineering analyses.

Accomplishments / Status

• Working 2D/3D air/water Navier-Stokes models based on front-capturing approaches.

• Working 1D/2D/3D macro-scale (porous media) air/water flow models using locally mass-conservative continuous and discontinuous finite element methods.

• Added surface integral approximations for jump conditions (e.g. surface tension).

• Spent five months at UT collaborating with various researchers on numerical and pore-/multi-scale modeling issues.

Accomplishments / Status

• Devised mass/volume conserving correction scheme needed for qualitative correctness, particularly for large surface tension.

• Implemented initial prototype of adaptive mesh refinement.

• Added initial support for flux limiters in discontinuous Galerkin finite element methods.

• Implemented fast-marching and fast-sweeping methods for level set redistancing.

• Parallelized code by leveraging Argonne’s Parallel Extensible Tookit for Scientific Computing (PETSc).

• Added higher-order adaptive time stepping by leveraging UNC’s Differential-Algebraic Equation Toolkit (DAETK).

Accomplishments / Status

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

Air bubble in water without conservation correction

Accomplishments / StatusAir bubble in water with conservation correction

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

Accomplishments / Status“Capillary tube” air/water without surface tension

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

Accomplishments / Status“Capillary tube” air/water with surface tension

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

Accomplishments / Status3D air bubble in water with surface tension (conservative level set method)

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

Accomplishments / StatusWater infiltrating into air-dry “cylinder packing”

Accomplishments / StatusWater infiltrating into air-dry “cylinder packing”

Accomplishments / StatusStokes flow of water in a sphere packing

Accomplishments / Status

Cross-section of a 3D tomographic image showingresidual water (blue), air (red), sand (green). Courtesy of Clint Willson, LSU.

Accomplishments / Status• Currently emphasis is on improving model

equations and robustness/flexibility of the implementation.– Surface tension representation in two-phase flows.– Contact line movement in three-phase flows.– Surface tension dominated flows are stiff and require

better time integration.– Memory usage, parallelism, computational kernel, and

front-end need additional work in order to achieve a multiscale capability.

Products

• Theoretical and computational frameworks for passing information between microscopic two-phase flow/particle systems to macroscopic variably saturated media.

• New constitutive models for macroscopic models and numerical multiscale models for macroscale engineering models.

Technology Transfer

• High-fidelity vessel effects(Kees and Farthing): Arbitrary Lagrangian-Eulerian mesh technology and porous structure theory/models.

• Countermine Phenomenology(Howington): Mesh generation capability and moisture distribution theory/models.

• Stress Transfer in Granular Media(Peters):Discrete Element method coupling and upscaling tools, surface tension theory/models.

Publications

• Non-Conforming Finite Elements for Air/Water Flow in Porous Media. Farthing and Kees. (In preparation 2008) Advances in Water Resources

• A conservative level-set method for two-phase flow with surface tension effects. Kees, Farthing, Dawson, and Prudhomme. (In preparation 2008) Journal of Computational Physics

• Locally Conservative, Stabilized Finite Element Methods for Variably-Saturated Flow. Kees, Farthing, and Dawson. (Accepted) Computer Methods in Applied Mechanics and Engineering

Publications

• USNCCM 2007 Minisymposium– Robust Nonlinear Iterative Methods for Time-Dependent Unsaturated

Flow. Kees, Farthing, et al.– Locally Conservative, Stabilized Finite Element Methods for Richards’

Equation. Farthing, Kees, et al.– A Computational Tool for Creating Synthetic, Smallscale Infrared

Imagery of Vegetated Soil Surfaces. Peters, Ballard, et al.

• Local Discontinuous Galerkin Approximations to Richards’ Equation. Li, Farthing, et al. Advances in Water Resources 30, 555-575 (2007).

• Adaptive Local Discontinuous Galerkin Approximations to Richards’ Equation. Li, Farthing, et al. Advances in Water Resources 30, 1883-1901. (2007).

• Clint Willson (LSU, Civil, Pore scale experiment)• David DiCarlo (UT, Petroleum, Pore scale experiment)• Graham Carey (UT, ICES, Finite elements)• Clint Dawson (UT, ICES, Finite elements)• Lea Jenkins (Clemson, Math, Time discretization)• John Chrispell (Tulane, Math, Time discretization)• Masa Prodanovic (UT, Pore scale modeling)• Tim Kelley (NCSU, Math, Solvers)• Casey Miller (UNC, Environmental, Macroscale

modeling)

Collaborations

Issues• Resources

– Need engineers and scientists with UNIX/HPC programming skills

– Fast, robust numerical software for parallel architectures (adequate use/understanding of existing tools)

• Scientific/Technical– Obtaining relevant experimental data and

incorporating into the models– Accurately modeling surface tension– Accurately modeling contact line dynamics and

statics– Conservation of mechanical energy and mass